The Toffees had a rare victory in a pulsating game at Elland Road thanks to goals from Gylfi Sigurdsson and England international Dominic Calvert-Lewin.
Ancelotti’s men had a dream start when Sigurdsson put them ahead nine minutes into the game, before their advantage was doubled on 41 minutes through Calvert-Lewin 12th league goal of the season.
The hosts halved the deficit three minutes after halftime thanks to Raphinha to lay a foundation for a comeback but the Merseyside-based club stuck to their guns and recorded their second ever Premier League win at Leeds.
"It's special because it was a difficult game against a difficult team. We did really well in the first half. Second half was more difficult because we conceded early. To arrive at the end of game was not easy,” Ancelotti told the media after the game.
"The sacrifice, concentration and motivation was good. I'm really pleased with the reaction after the Newcastle defeat.”
"The plan was to be intelligent in the game and defend well and find the opportunity to counter-attack. They push a lot of players in front.
"We lost a little bit of confidence after the goal. But this team is showing when they defend we are comfortable.
"We have better luck away from home. I hope [next opponents] Manchester United scored all their goals against Southampton."